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Simplifying 4.9x2 + 14x + 0 = 12 Reorder the terms: 0 + 14x + 4.9x2 = 12 Remove the zero: 14x + 4.9x2 = 12 Solving 14x + 4.9x2 = 12 Solving for variable 'x'. Reorder the terms: -12 + 14x + 4.9x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + 14x + 4.9x2 = 0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -2.448979592 + 2.857142857x + x2 = 0 Move the constant term to the right: Add '2.448979592' to each side of the equation. -2.448979592 + 2.857142857x + 2.448979592 + x2 = 0 + 2.448979592 Reorder the terms: -2.448979592 + 2.448979592 + 2.857142857x + x2 = 0 + 2.448979592 Combine like terms: -2.448979592 + 2.448979592 = 0.000000000 0.000000000 + 2.857142857x + x2 = 0 + 2.448979592 2.857142857x + x2 = 0 + 2.448979592 Combine like terms: 0 + 2.448979592 = 2.448979592 2.857142857x + x2 = 2.448979592 The x term is 2.857142857x. Take half its coefficient (1.428571429). Square it (2.040816328) and add it to both sides. Add '2.040816328' to each side of the equation. 2.857142857x + 2.040816328 + x2 = 2.448979592 + 2.040816328 Reorder the terms: 2.040816328 + 2.857142857x + x2 = 2.448979592 + 2.040816328 Combine like terms: 2.448979592 + 2.040816328 = 4.48979592 2.040816328 + 2.857142857x + x2 = 4.48979592 Factor a perfect square on the left side: (x + 1.428571429)(x + 1.428571429) = 4.48979592 Calculate the square root of the right side: 2.118913854 Break this problem into two subproblems by setting (x + 1.428571429) equal to 2.118913854 and -2.118913854.Subproblem 1
x + 1.428571429 = 2.118913854 Simplifying x + 1.428571429 = 2.118913854 Reorder the terms: 1.428571429 + x = 2.118913854 Solving 1.428571429 + x = 2.118913854 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.428571429' to each side of the equation. 1.428571429 + -1.428571429 + x = 2.118913854 + -1.428571429 Combine like terms: 1.428571429 + -1.428571429 = 0.000000000 0.000000000 + x = 2.118913854 + -1.428571429 x = 2.118913854 + -1.428571429 Combine like terms: 2.118913854 + -1.428571429 = 0.690342425 x = 0.690342425 Simplifying x = 0.690342425Subproblem 2
x + 1.428571429 = -2.118913854 Simplifying x + 1.428571429 = -2.118913854 Reorder the terms: 1.428571429 + x = -2.118913854 Solving 1.428571429 + x = -2.118913854 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.428571429' to each side of the equation. 1.428571429 + -1.428571429 + x = -2.118913854 + -1.428571429 Combine like terms: 1.428571429 + -1.428571429 = 0.000000000 0.000000000 + x = -2.118913854 + -1.428571429 x = -2.118913854 + -1.428571429 Combine like terms: -2.118913854 + -1.428571429 = -3.547485283 x = -3.547485283 Simplifying x = -3.547485283Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.690342425, -3.547485283}
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